Empirical Bayes estimation of the parameter vector θ=(β^1,σ^2)' in a multiple linear regression model Y=Xβ+ε is considered, where β is the vector of regreasion coeffcient, ε-N(0,σ^2I) with σ^2 unknown. In...
详细信息
Empirical Bayes estimation of the parameter vector θ=(β^1,σ^2)' in a multiple linear regression model Y=Xβ+ε is considered, where β is the vector of regreasion coeffcient, ε-N(0,σ^2I) with σ^2 unknown. In this paper, we construct the EB estimators of θ by using the kernel estimation of multivariate density function and its partial derivatives, Uuder some momeut couditions on prior distribution we obtain their asymptotic optimality.
The purpose of this study was to relate the distribution of corn ( Zea mays L.) roots to depth of a declining water table in a sandy soil association. Knowledge of root response to declining water tables is important ...
详细信息
The purpose of this study was to relate the distribution of corn ( Zea mays L.) roots to depth of a declining water table in a sandy soil association. Knowledge of root response to declining water tables is important for proper crop production management. Roots from 10 monoliths (91 cm deep), centered over and perpendicular to the corn row, were obtained at about full silk (August 26) from corn growing in 91-cm rows. Water table depths ranged from 1.33 to 2.64 m at silking after declining at the rate of about 1.3 cm/day since July 1. About 20% of the evapotranspiration was supplied by natural precipitation with the remaining 80% from soil water depletion and the water table for the period from July 1 to September 16 (final harvest). Shoot growth was maximum at intermediate water table depths. An equation describing root distribution was obtained from a regression fit of root depth (Y) as a function of water table depth (X 1 ) and cumulative root weight (X 2 ). A similar fit was made using root length as X 2 . In no case was more than 10% of the total measured root weight or more than 20% of the total measured root length below 75 cm. The distribution of roots with depth indicates water requirements for corn in these sandy soils must be supplied to a root zone with maximum depth of about 100 cm. Retarded root growth was observed where soil oxygen diffusion rate (O.D.R.) was less than 26 g/cm 2 /10 8 min. Such O.D.R. values were obtained at depths greater than 30 cm at the shallow water table site. Apparent normal root development occurred when O.D.R. values were greater than 30 g/cm 2 /10 8 min and matric suctions were about 100 mb.
SUMMARY: A basic model of factor analysis is employed in the estimation of multiple correlation coefficients and partial regression weights. Estimators are derived for situations in which some or all of the independen...
详细信息
暂无评论